an update from the nysed office of curriculum & instruction amtnys november 2012

www.engageNY.orgwww.engageNY.org

An Update from the NYSED Office of Curriculum & Instruction

AMTNYS November 2012Mary Cahill, Director

John Svendsen, Associate in Mathematics

www.engageNY.orgwww.engageNY.org 2

Agenda

• Why the change in standards

• Brief overview of the shifts required by the NYS P-12 Common Core Learning Standards for Mathematics

• Opportunity for questions


“Our country is in a slow decline, just slow enough for us to be able to pretend - or believe - that a decline is not taking place.”

“Our problem is us - what we are doing and not doing, how our political system is functioning and not functioning, which values we are and are not living by.”

Friedman & Mandelbaum – That Used to Be Us

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High School Graduation & College Completion• Nationally, out of 100 middle school students…

‒93 say they want to go to college.

‒70 will graduate from high school.

‒44 enroll in college.

‒26 earn a college degree within six years

Conley, David. 2012, “The Complexities of College and Career Readiness.” https://epiconline.org/files/pdf/07102012_Keene_NH.pdf


Our Challenge

Graduating All Students College & Career Ready

New York's 4-year high school graduation rate is 74% for All Students

However, the gaps are disturbing.

June 2011 Graduation Rate

Graduation under Current Requirements Calculated College and Career Ready*

% Graduating % Graduating

All Students 74.0 All Students 34.7

American Indian 59.6 American Indian 16.8

Asian/Pacific Islander 82.4 Asian/Pacific Islander 55.9

Black 58.4 Black 11.5

Hispanic 58.0 Hispanic 14.5

White 85.1 White 48.1

English Language Learners 38.2 English Language Learners 6.5

Students with Disabilities 44.6 Students with Disabilities 4.4

*Students graduating with at least a score of 75 on Regents English and 80 on a Math Regents, which correlates with success in first-year college courses.

Source: NYSED Office of Information and Reporting Services

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College Instructors and Employers Say GraduatesAre Not Prepared for College and Work

Average estimated proportions of recent high school graduates who are not prepared

42% 45%

0%

25%

50%

75%

100%

College Instructors Employers

Source: Peter D. Hart Research Associates/Public Opinion Strategies, Rising to the Challenge: Are HighSchool Graduates Prepared for College and Work? prepared for Achieve, Inc., 2005.

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College Graduation and Remediation Rates

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The more remedial classes students take, the less likely they are to stay in college.


Higher Education Has Never Mattered More

Unemployment Rate By Degree: 2010 Median Annual Earnings by Educational Degree: 2010

1.9%

5.4%

2.4%

4.0%

7.0%

9.2%

10.3%

14.9%

$83,720

$80,600

$23,088

$32,552

$37,024

$39,884

$53,976

$66,144

No HS Diploma

HS Diploma

Some College, No Degree

Associate

Bachelors

Masters

Doctorate

Professional Degree

Education pays in higher overall earnings and lower unemployment rates.SOURCE: 2010 Bureau of Labor Statistics, Current Population Survey

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International Competitiveness

Sources: Pathways to Prosperity Project, Harvard University, February 2011; Organization for Economic Cooperation and Development.

The U.S. has fallen from 1st place to 13th place in high school graduation

Note: Approximated by percentage of persons with upper secondary or equivalent qualifications in the age groups 55-64, 45-54, 35-44, and 25-34 years.



College Completion Rank Declining: Percentage of 25- to 34-Year-Olds with an Associate Degree or Higher, 2007

Sources: Pathways to Prosperity Project, Harvard University, February 2011; College Board, The College Completion Agenda 2010 Progress Report, 2010; Organization for Economic Cooperation and Development.


Job Readiness

Labor Market Has Become More Demanding

Sources: Pathways to Prosperity Project, Harvard University, February 2011; Georgetown Center on Education and the Workforce, Help Wanted: Projections of Jobs and Education

Requirements Through 2018, June 2010.

A post-secondary education is the“Passport to the American Dream”:

Of the projected 47 million job openings between 2009-2018, nearly two-thirds will require workers to have at least some post-secondary education.

14 million job openings will go to people with an associate’s degree or occupational certificate and pay a significant premium over many jobs open to those with just a high school degree.


Job Readiness

College Completion is Crucial for Employment

Since 1973, jobs that require at least some college have exploded while opportunities for those with just a high school education have shrunk

dramatically

Source: Pathways to Prosperity Project, Harvard University, February 2011, http://www.gse.harvard.edu/news_events/features/2011/Pathways_to_Prosperity_Feb2011.pdf



College and university graduation rates in 1995 and 2006 (first-time graduation)

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1. Net graduation rate is calculated by summing the graduation rates by single year of age in 2006.2. Year of reference 2005.Countries are ranked in descending order of the graduation rates for tertiary-type A education in 2006.Source: OECD. Table A3.2 See Annex 3 for notes (www.oecd.org/edu/eag2008 )

%

2nd

15th

Decline in relative position of U.S. from 1995

to 2006

These Standards are not intended to be new

names for old ways of doing business. They

are a call to take the next step. … It is time to

recognize that standards are not just promises

to our children, but promises we intend to

keep.

CCSSM, p. 5


Principles of the CCSS

Aligned to requirements for college and career readiness

Based on evidence

Honest about time


Some Old Ways of Doing Business (1 of 2)

• A different topic every day

• Every topic treated as equally important

• Elementary students dipping into advanced topics at the expense of mastering fundamentals

• Infinitesimal advance in each grade; endless review

• Incoherence and illogic – bizarre associations, or lacking a thread

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Some Old Ways of Doing Business (2 of 2)

• Lack of rigor

• Reliance on rote learning at expense of concepts

• Aversion to repetitious practice

• Severe restriction to stereotyped problems lending themselves to mnemonics or tricks

• Lack of quality applied problems and real-world contexts

• Lack of variety in what students produce– E.g., overwhelmingly only answers are produced, not arguments, diagrams, models, etc.

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From.... To….

856 = ___ hundreds, ___ tens, ___ ones

1 hundredth = ___ tenths

x2 – 10x + 21 = 0 ¾ c(c –1) = c


• Focus strongly where the standards focus

• Coherence: Think across grades and link to major topics within grades

• Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application with equal intensity

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The Three Instructional Shifts Demanded by the Core


Mathematics Shift 1: FocusWhat the Student Does… What the Teacher Does…•Spend more time on fewer concepts.

•excise content from the curriculum

•Focus instructional time on priority concepts

•Give students the gift of time

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Shift #1 in Research

“Move away from "mile wide, inch deep" curricula identified in TIMSS.”Ginsburg et al., 2005

“Although high school English standards and courses tend to emphasize literature, most of the reading students will encounter

in college or on the job is informational in nature (e.g., textbooks, manuals, articles, briefs and essays).”

Achieve, Inc. http:// www.achieve.org/files/50-s tate-07-Final.pdf

Students need sustained exposure to expository text to develop important reading strategies

Afflerbach, Pearson, & Paris, 2008; Kintsch, 1998, 2009; McNamara, Graesser, & Louwerse, in press; Perfetti, Landi, & Oakhill, 2005; van den Broek et al.,

2001; van den Broek et. al, 1995

Shift #1 in Research

“Move away from "mile wide, inch deep" curricula identified in TIMSS.”Ginsburg et al., 2005

“Although high school English standards and courses tend to emphasize literature, most of the reading students will encounter

in college or on the job is informational in nature (e.g., textbooks, manuals, articles, briefs and essays).”

Achieve, Inc. http:// www.achieve.org/files/50-s tate-07-Final.pdf

Students need sustained exposure to expository text to develop important reading strategies

Afflerbach, Pearson, & Paris, 2008; Kintsch, 1998, 2009; McNamara, Graesser, & Louwerse, in press; Perfetti, Landi, & Oakhill, 2005; van den Broek et al.,

2001; van den Broek et. al, 1995


GradeFocus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

K–2Addition and subtraction - concepts, skills, and problem solving and place value

3–5Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving

6Ratios and proportional reasoning; early expressions and equations

7Ratios and proportional reasoning; arithmetic of rational numbers

8 Linear algebra and linear functions

Key Areas of Focus in Mathematics


Major Areas of Work: P-2

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Grade Major Areas of Work

K Counting and Cardinality•Know number names and count sequence•Count to tell the number of objects.•Compare numbers.

Operations and Algebraic Thinking•Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Number and Operations in Base Ten•Work with numbers 11-19 to grain foundations for place value.

1 Operations and Algebraic Thinking•Represent and solve problems involving addition and subtraction.•Understand and apply properties of operations and the relationship between addition and subtraction.•Add and subtract within 20.•Work with addition and subtraction equations.

Number and Operations in Base Ten•Extend the counting sequence.•Understand place value.•Use place value understanding and properties of operations to add and subtract.

Measurement and Data•Measure lengths indirectly by iterating length units.

2 Operations and Algebraic Thinking•Represent and solve problems involving addition and subtraction.•Add and subtract within 20.•Work with equal groups of objects to gain foundations for multiplication.

Number and Operations in Base Ten•Understand place value.•Use place value understanding and properties of operations to add and subtract.

Measurement and Data•Measure and estimate lengths in standard units.•Relate addition and subtraction to length.


Major Areas of Work: 3-5

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3 Operations and Algebraic Thinking•Represent and solve problems involving multiplication and division.•Understand the properties of multiplication and the relationship between multiplication and division.•Multiply and divide within 100.•Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Number and Operations - Fractions•Develop understanding of fractions as numbers.

Measurement and Data•Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.•Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

4 Operations and Algebraic Thinking•Use the four operations with whole numbers to solve problems.

Number and Operations in Base Ten•Generalize place value understanding for multi-digit whole numbers.•Use place value understanding and properties of operations to perform multi-digit arithmetic.

Number and Operations - Fractions•Extend understanding of fraction equivalence and ordering.•Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. •Understand decimal notation for fractions, and compare decimal fractions.

5 Number and Operations in Base Ten•Understand the place value system.•Perform operations with multi-digit whole numbers and with decimals to hundredths.

Number and Operations - Fractions•Use equivalent fractions as a strategy to add and subtract fractions.•Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Measurement and Data•Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.


Major Areas of Work: 6-8

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6 Ratios and Proportional Relationships•Understand ratio concepts and use ratio reasoning to solve problems.

The Number System•Apply and extend previous understandings of numbers to the system of rational numbers.•Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Expressions and Equations•Apply and extend previous understandings of arithmetic to algebraic expressions.•Reason about and solve one variable equations and inequalities.•Represent and analyze quantitative relationships between dependent and independent variables.

7 Ratios and Proportional Relationships•Analyze proportional relationships and use them to solve real-world and mathematical problems.

The Number System•Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Expressions and Equations•Use properties of operations to generate equivalent expressions.•Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

8 Expressions and Equations•Work with radicals and integer exponents.•Understand the connections between proportional relationships, lines, and linear equations.•Analyze and solve linear equations and pairs of simultaneous linear equations.

Functions•Define, evaluate, and compare functions.

Geometry•Understand and apply the Pythagorean theorem.•Understand congruence and similarity using physical models, transparencies, or geometry software.


Sample Grade 5

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Mathematics Shift 2: Coherence

What the Student Does… What the Teacher Does…•Build on knowledge from year to year, in a coherent learning progression

•Connect the threads of math focus areas across grade levels

•connect to the way content was taught the year before and the years after

•Focus on priority progressions

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Shift 2 in Research:

“The coherence and sequential nature of mathematics dictate the foundational skills that

are necessary for the learning of algebra. The most important foundational skill not

presently developed appears to be proficiency with fractions (including decimals, percents,

and negative fractions). Final Report of the National Mathematics Advisory Panel (2008, p. 18)

Shift 2 in Research:

“The coherence and sequential nature of mathematics dictate the foundational skills that

are necessary for the learning of algebra. The most important foundational skill not

presently developed appears to be proficiency with fractions (including decimals, percents,

and negative fractions). Final Report of the National Mathematics Advisory Panel (2008, p. 18)


Mathematics topics

intended at each grade by

at least two-thirds of A+

countries

Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states

The shape of math in A+ countries

1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).

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K 12

Number and Operations

Measurement and Geometry

Algebra and Functions

Statistics and Probability

Traditional U.S. Approach


Focusing Attention Within Number and Operations

Operations and Algebraic Thinking

Expressions and Equations

Algebra

→ →

Number and Operations—Base Ten

→

The Number System

→

Number and Operations—Fractions

→

K 1 2 3 4 5 6 7 8 High School


Mathematics Shift 3: Rigor through FluencyWhat the Student Does… What the Teacher Does…

•Spend time practicing, with intensity, skills (in high volume)

•Push students to know basic skills at a greater level of fluency

•Focus on the listed fluencies by grade level

•Uses high quality problem sets, in high volume

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Use should be made of what is clearly known from rigorous research about how children learn, especially by recognizing a) the

advantages for children in having a strong start; b) the mutually reinforcing benefits of conceptual understanding, procedural fluency, and

automatic (i.e., quick and effortless) recall of facts; and c) that effort, not just inherent talent, counts in mathematical achievement.

-Foundations for Success The Final Report of the National Mathematics Advisory Panel, 2008

Use should be made of what is clearly known from rigorous research about how children learn, especially by recognizing a) the

advantages for children in having a strong start; b) the mutually reinforcing benefits of conceptual understanding, procedural fluency, and

automatic (i.e., quick and effortless) recall of facts; and c) that effort, not just inherent talent, counts in mathematical achievement.



Key FluenciesGrade Required Fluency

K Add/subtract within 5

1 Add/subtract within 10

2Add/subtract within 20

Add/subtract within 100 (pencil and paper)

3Multiply/divide within 100

Add/subtract within 1000

4 Add/subtract within 1,000,000

5 Multi-digit multiplication

6Multi-digit division

Multi-digit decimal operations

7 Solve px + q = r, p(x + q) = r

8Solve simple 22 systems by inspection


Math Shift 4: Rigor through Deep UnderstandingWhat the Student Does… What the Teacher Does…

•Show mastery of material at a deep level

•Articulate mathematical reasoning

•demonstrate deep conceptual understanding of priority concepts

•Create opportunities for students to understand the “answer” from a variety of access points

•Ensure that EVERY student GETS IT before moving on

•Get smarter in concepts being taught

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Shift 4 in Research

Research has shown that learners become more engaged in the learning process when they are asked to explain and reflect on their

thinking processes.

-Surbeck, 1994; Good & Whang, 1999; Hettich, 1976

Researchers have found that students’ conceptual understanding and problem-solving skills improve when they are encouraged to

make sense of mathematics by writing about… their mathematical thinking.

-Putnam, 2003

Shift 4 in Research

Research has shown that learners become more engaged in the learning process when they are asked to explain and reflect on their

thinking processes.

-Surbeck, 1994; Good & Whang, 1999; Hettich, 1976

Researchers have found that students’ conceptual understanding and problem-solving skills improve when they are encouraged to

make sense of mathematics by writing about… their mathematical thinking.

-Putnam, 2003


Mathematics Shift 5: Rigor through ApplicationWhat the Student Does… What the Teacher Does…

•Apply math in other content areas and situations, as relevant

•Choose the right math concept to solve a problem when not necessarily prompted to do so

•Apply math including areas where its not directly required (i.e. in science)

•Provide students with real world experiences and opportunities to apply what they have learned

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Principal’s Role:

Ensure that math has a place in science instruction

Create a culture of math application across the school

Principal’s Role:

Ensure that math has a place in science instruction

Create a culture of math application across the school


Mathematics Shift 6: Rigor through Dual IntensityWhat the Student Does… What the Teacher Does…

•Practice math skills with an intensity that results in fluency

•Practice math concepts with an intensity that forces application in novel situations

•Find the dual intensity between understanding and practice within different periods or different units

•Be ambitious in demands for fluency and practice, as well as the range of application

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Research #6:

Use should be made of what is clearly known from rigorous research about how children learn, especially by

recognizing a) the advantages for children in having a strong start; b) the mutually reinforcing benefits of

conceptual understanding, procedural fluency, and automatic (i.e., quick and effortless) recall of facts; and c) that

effort, not just inherent talent, counts in mathematical achievement.


Research #6:

Use should be made of what is clearly known from rigorous research about how children learn, especially by

recognizing a) the advantages for children in having a strong start; b) the mutually reinforcing benefits of

conceptual understanding, procedural fluency, and automatic (i.e., quick and effortless) recall of facts; and c) that

effort, not just inherent talent, counts in mathematical achievement.



Shifts in Assessments

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Thank You

Mary Cahill [email protected] Svendsen [email protected]

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More Questions?

Office of State Assessment [email protected]

Teacher Evaluation (APPR), Student Learning

Objectives (SLO) [email protected]

Teacher Certification http://www.highered.nysed.gov/tcert/contact.ht

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WEBSITES

• Engageny• http://engageny.org/ • • PARCC Model Content Frameworks 3-11/Content

Emphases• http://www.parcconline.org/parcc-model-content-frameworks • • PreK-2 Content Emphases• http://engageny.org/wp-content/uploads/2012/03/nys-math-

emphases-k-8.pdf • • Common Core Toolkit (includes Mathematics toolkit)• http://engageny.org/resource/common-core-toolkit/ • •

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an update from the nysed office of curriculum & instruction amtnys november 2012

Documents

core engageny

reading students

orgsome old ways

mathematicsgradefocus

major topics

importantelementary

students producee

standards focuscoherence